i.e., the coefficient of absolute expansion of mercury is equal to the coefficient of apparent expansion of mercury in glass, increased by the coefficient of cubical expansion of glass.

According to Regnault, the mean value of m for temperature between o° and 100° is '000180...

Hence this value, together with the value determined for the coefficient of apparent expansion of mercury in glass, will suffice to determine the coefficient of cubical expansion of glass.

To determine the coefficient of absolute expansion of water, &c.

EXPT. 16.-The same bottle as that used for the last experiment is emptied, cleaned with nitric acid, and finally filled with water. It is then immersed in a beaker of water, which is boiled for some time, until all the air dissolved in the contained water has been expelled.

The temperature of the water in the beaker is then maintained constant at about 80° C. for a space of 8 or 10 minutes, when the water surface in the bottle is adjusted to be level with the scratch, and the bottle is removed from the beaker, dried, and weighed. The weighing may be performed

on a sensitive chemical balance, but the bottle should first be allowed to cool, as the currents of air set in motion by the hot bottle will produce errors.

Similar operations may be performed at 70°, 60°, 30°, 20°, 10°, 0° C., the water in the beaker being cooled with ice shavings for the last experiments. Finally, the coefficients of expansion for these various values may be calculated, using the previously determined value of the coefficient of expansion of glass.

EXPT. 17.-The expansion of water can also be determined in another manner. A glass bulb about 2 in. in diameter is weighted with shot till

FIG.

34.Weighted glass bulb, for determining expansion of a liquid.

it will just sink in cold water. The neck of the bottle is then drawn out and sealed, and the drawn out portion bent into a hook (Fig. 34). The bulb is suspended by means of a horsehair from the

beam of a balance, and weighed. A small three-legged table is then placed above one of the balance pans, and a beaker of hot water is supported on this, so that the bulb is entirely immersed when the beam is swinging (Fig. 35).

Fig. 35.-Arrangement for determining the expansion of a liquid by weighing a body of known expansibility in it.

Obtain the apparent masses of the bulb when suspended in water at two or three different temperatures, and deduce the mass of the water displaced in each instance.

true mass of bulb.

apparent mass of bulb suspended in water at temp. t,° C.

coefficient of cubical expansion of glass. ρ the (unknown) density of water at 4° C.

=

(W W1) grams.

{

1 + 8(42 − h) }

(WW) grams.

C.CS.

If this mass of water were cooled to t1° C., it would occupy a volume

C.CS. But at t° C. it actually occupied a volume of

... Increase in volume of

1 {1 + g (t2 - t1)} c.cs.

c.cs. of water, when heated through

W +

g (t2- t1).

... Increase in volume of I c.c. of water when heated through

Further, the quantity by which g is multiplied will be very nearly equal Hence, finally, if ẞ is the mean coefficient of absolute expansion, of water between t1° and to° C.,

to I.

Experiments to determine the behaviour of water with regard to expansion, between the temperature 0--10°, will be described later on in this chapter.

Coefficient of Absolute Expansion of Mercury.Before giving an account of Regnault's experimental determination of the absolute expansion of mercury, a simple modification of the apparatus previously used by Dulong and Petit for the same purpose will be described. This apparatus can be made, with the exercise of a little care, by any one possessing a slight amount of skill in bending glass tubing, and will permit of tolerably accurate results being obtained.

The immediate object of this experiment is to determine the ratio of the densities of mercury at two different temperatures. Having obtained this, a simple calculation will suffice to determine the coefficient of expansion.

Now the ratio of the densities of two liquids, such for instance as mercury and water, may be obtained by pouring mercury into a U-tube, and then introducing a column of water into one of the limbs above the mercury. If we imagine a

horizontal plane to be drawn through the surface of separation of the water and mercury, this plane will cut off a short column of mercury in the other limb of the tube, the height of this column being such that the pressure due to it is just equal to the pressure

a

1

produced by the water column. It must be remembered that pressure denotes force per square cm. ; hence the pressure produced by column of water H1 cm. high is obviously equal to the force exerted by gravity on a column of water of I sq. cm. sectional area, and H1 cms. long. This force is equal to g× 1 × H1 = gH1 dynes where g is the acceleration due to gravity. Similarly, if p is the density of mercury the pressure due to a column of mercury H, cms. high will be equal to gpH.

The condition that these pressures should be equal, gives

columns should produce equal the heights of the columns densities.

gpH = gH1 or pH2 = H1. Hence the condition that two liquid pressures, is obtained by equating multiplied by their respective

It will be noticed that no error is introduced into this result by irregularities in the sectional areas of the limbs, or even if any variations in the dimensions of the limbs occur during the course of the experiment.

The application of this principle to the determination of the absolute expansion of mercury may best be explained when the construction of the necessary apparatus has been described.

Fig. 37 shows front and side views of the apparatus. It may be constructed as follows:--

EXPT. 18.-A wooden stand, consisting of a base 6" x 9", and an upright board 24′′ × 9′′, is made from 4-inch pine. Four blocks, about I" x 2" x 3", are provided, and are ultimately fixed in the positions

Each

A1 A2 A3 A4 (Fig. 37). These blocks are slightly grooved on their front surfaces, so as to admit of the pieces of 1" glass tubing T1, T2 being fastened to them at a distance of 7" from centre to centre. of the glass tubes T1, T2, is 18" long, and is provided at both ends with sound corks. Each cork is bored centrally to take a glass tube of about "internal diameter, and excentrically to take another tube of rather smaller size.

The most important part of the apparatus is the continuous glass tube BCDEFG. A piece of "glass tubing 5 feet long is taken and cleaned by drawing through it a small plug of wet cotton wool attached to the end of a string. The tube is dried by gently heating and drawing air through it, and then twice bent at right angles at D and E, two points 7" apart and equidistant from the middle of the piece of tubing. Care should be